RELAXATION-TIME SPECTRUM FOR A HYDROGEN RELAXATION PEAK IN A Nb-50-at. %-V ALLOY

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RELAXATION-TIME SPECTRUM FOR A

HYDROGEN RELAXATION PEAK IN A Nb-50-at.

%-V ALLOY

J. Cost, C. Snead, Jr., J. Bethin

To cite this version:

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RELAXATION-TIME SPECTRUM FOR A HYDROGEN RELAXATION PEAK IN

A

Nb-50-at. %-V ALLOY

J.R. COST, C.L. SNEAD'

,

**Jr*. and**

J.

BETHIN++

Material Science and Technology Division, Los Alamos National

Laboratory, Los Alamos, N.M. 87545, U.S.A.

'Brookhaven National Laboratory, Upton ,

N.Y.

11973, B.S.A.

A b s t r a c t

-

I n t e r n a l f r i c t i o n has been measured vs. temperature from 15-330 K f o r equiatomic Nb-V a l l o y s with up to 28 a t . % H. A broad peak a t roughly 125 K shows c h a r a c t e r i s t i c s which s t r o n g l y s u g g e s t t h a t i t i s a r e o r i e n t a t i o n

peak. D e t a i l e d a n a l y s i s using a newly developed method i n d i c a t e s the a c t i v a - t i o n energy spectrum t o be b e l l shapedl$nd t o be over the range 0.10 t o 0.30 eV. A p r e - e x p o n e n t i a l f a c t o r of 5x10- i s determined.

I

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INTRODUCTION

Controversy has developed concerning whether i n t e r s t i t i a l hydrogen i n bcc m e t a l s shows a Snoek r e l a x a t i o n which may be observed by measuring the i n t e r n a l f r i c t i o n vs. temperature. Evidence f o r t h i s has been d i f f i c u l t to o b t a i n because most bcc metals tend t o form h y d r i d e s a t the temperatures a t which a Snoek peak might be expected. R e c e n t l y , however, Tanaka and Koiwa /1/ have r e p o r t e d a hydrogen Snoek peak f o r Nb-3.9 a t . % T i a l l o y . Subsequently, Owen, Buck and S c o t t /2/ p r e s e n t e d evidence f o r a peak due t o hydrogen i n an equiatomic Nb-V a l l o y b u t they were n o t a b l e to f u l l y observe t h e peak due t o t h e l i m i t e d temperature range of t h e i r equip- ment. I n t h i s paper t h e hydrogen peak i n t h i s l a t t e r a l l o y is measured over t h e f u l l temperature range of t h e peak. Also, a new method of a n a l y s i s i s used which provides d e t a i l e d i n f o r m a t i o n about the spectrum of r e l a x a t i o n times (and a c t i v a t i o n e n e r g i e s ) r e s p o n s i b l e f o r t h e peak.

I1

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EXPERIMENTAL METHODS

Alloy samples were made from 99.99 a t . % Nb and V rod. Charges of about 8 g were a r c melted. A f t e r r g l l i n g t o a t h i c k f o i l (0.5 mm), bars were spark c u t t o a f i n a l shape of 12x2x0.3 mm

.

Samples were then annealed and r i g o r o u s l y p u r i f i e d of oxy- gen, n i t r o g e n , and carbon by wrapping i n T i f o i l and holding i n an i n e r t atmosphere a t llOO°C f o r 7 days. A f t e r removing a l l Ti i n an a c i d e t c h , samples were charged w i t h H. I n an a l l - s t a i n l e s s , high-vacuum system of c a l i b r a t e d volume, each sample was heated t o 800°C, a known volume and p r e s s u r e of H2 a d m i t t e d , and t h e sample cooled slowly i n the range 300-500°. H c o n c e n t r a t i o n s were c a l c u l a t e d from t h e p r e s s u r e change and checked l a t e r by degassing a f t e r the i n t e r n a l - f r i c t i o n measurements. F o i l s were then v i b r a t e d i n f l e x u r e i n e t h e r t h e i r fundamental o r f i r s t

₁₆

overtone t o s t r a i n amplitudes of l e s s than 5x10-

.

The fm d e t e c t i o n and d a t a log- ging of

6

and t h e frequency ( f o r modulus-change measurement) were s t a n d a r d phase- locked loop and minicomputer sys tems.

111

-

RESULTS

Shown i n Fig. 1 i s a p l o t of i n t e r n a l f r i c t i o n vs. r e c i p r o c a l temperature measured a t two d i f f e r e n t f r e q u e n c i e s f o r an equiatomic Nb-V a l l o y with 8.0 atomic p e r c e n t hydrogen. The peak temperatures f o r t h e s e two measurements a r e roughly 120 and 130 K. The d a t a a r e c o r r e c t e d f o r background damping, the d i f f e r e n c e between t h e l o g r i t h m i c decrement and i n t e r n a l f r i c t i o n , t h e v a r i a t i o n of the measurement

"Present address

:

Grumman Corp., Bethpage, N.Y.

11714, U.S.A.

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f r e q u e n c y w i t h t e m p e r a t u r e , and t h e temperature dependence o f t h e r e l a x a t i o n s t r e n g t h described by W e l l e r , e t a l . / 3 / . As shown by t h e Debye peak a t 130 K , t h e i n t e r n a l f r i c t i o n peaks a t b o t h f r e q u e n c i e s a r e wider by more than a f a c t o r o f t h r e e than p r e d i c t e d f o r a s i n g l e r e l a x a t i o n t i m e .

As w i l l be d i s c u s s e d , t h e c h a r a c t e r i s t i c s o f t h e s e peaks a r e c o n s i s t e n t w i t h t h o s e f o r c l a s s i c a l Snoek peaks; i.e., t h e y are due t o t h e s t r e s s - i n d u c e d motion o f i n t e r - s t i t i a l hydrogen. Evidence f o r t h i s i s shown i n Fig. 2 i n which t h e v a r i a t i o n o f t h e maximum peak h e i g h t w i t h c o n c e n t r a t i o n o f hydrogen i s p l o t t e d . I t may be seen t h a t t h i s v a r i a t i o n i s l i n e a r a s expected f o r a Snoek-type r e l a x a t i o n . The r e l a x a - t i o n s t r e n g t h (6,, =

k c o )

f o r t h e hydrogen r e l a x a t i o n i s 0.006 a t . %. The s i g n i f i c a n c e o f t h i s v a l u e as it r e l a t e s t o s i t e occupancy w i l l be d i s c u s s e d elsewhere. TEMPERATURE ( K l 0,060300 200 150 120 100 90 80 Nb 246

"

246 H8.0

Fig. 1

-

I n t e r n a l f r i c t i o n v s . temperature Fig. 2.

-

Modulus d e f e c t ( s o l i d ) f o r Nb-V a l l o y w i t h 8.0 a t . % H measured a t and 6max ( o p e n ) as a f u n c t i o n two d i f f e r e n t f r e q u e n c i e s An e q u i v a l e n t o f CH.

Debye peak f o r ~ 2 6 6 4 0 s" i s shown. The s o l i d l i n e s through t h e data a r e from t h e DSA method.

I t i s reasonable t o assume t h a t t h e r e l a t i v e l y l a r g e w i d t h o f t h i s peak i s due t o t h e f a c t t h a t a wide d i s t r i b u t i o n o f r e l a x a t i o n t i m e s i s i n v o l v e d i n t h e r e l a x a - t i o n . As d i s c u s s e d by Nowick and Berry / 4 / , such a d i s t r i b u t i o n may be due t o a d i s t r i b u t i o n o f a c t i v a t i o n e n e r g i e s or o f p r e - e x p o n e n t i a l s o r a combination o f both. I f we assume a d i s t r i b u t i o n o f a c t i v a t i o n e n e r g i e s , t h e n t h e amount o f s h i f t o f t h e peaks w i t h frequency w i l l v a r y w i t h temperature and may be measured t o o b t a i n an i n d i c a t i o n o f t h e spread o f a c t i v a t i o n e n e r g i e s f o r t h e two measurement frequen- c i e s

in

Fig. 1. C a l c u l a t e d v a l u e s f o r Q e f f are i n t h e range from roughly 0.15 t o 0.25 eV. The a c t i v a t i o n energy corresponding t o t h e peak maximum i s 0.205 eV, which may be t a k e n as roughly t h e c e n t e r o f t h e a c t i v a t i o n energy spectrum. From t h i s c e n t r a l a c t i v a t i o n e n e r g y , t h e Arrhenius r e l a t n , and t h e approximation t h a t , a t t h e peak temperature U-1, we t h e n o b t a i n ~ ~ - 5 ~ 1 0 ' ~ ~ s f o r t h e p r e - e x p o n e n t i a l f a c t o r . IV

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DIRECT SPECTRUM ANALYSIS

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The d a t a shown i n Fig. 1 have been analyzed using two d i f f e r e n t v e r s i o n s of t h e DSA method which r e p r e s e n t two extreme models of t h e p h y s i c a l s i t u a t i o n : ( i ) I t i s assumed t h a t the b r e a d t h of the r e l a x a t i o n - t i m e spectrum i s only due t o a d i s t r i b u - t i o n of a c t i v a t i o n e n e r g i e s with a c o n s t a n t p r e - e x p o n e n t i a l f a c t o r . ( i i ) The oppo- s i t e of t h e above i s assumed. The e s t i m a t e of the r e l a x a t i o n - t i m e ( o r a c t i v a t i o n energy) spectrum using t h e DSA a n a l y s i g f o r the f i r s t of t h e s e c o n d i t i o n s i s shown i n Fig. 3 f o r t h e data with ~ 2 6 6 4 0 s'

.

Here t h e histogram is c a l c u l a t e d f o r peak temperature, 130 K, and the v a l u e of the p r e - e x p o n e n t i a l i s taken a s 5x10-

r

S"

s. The s c a l e of d i s t r i b u t i o n of a c t i v a t i o n e n e r g i e s i s shown a c r o s s the top of t h e f i g u r e . I t may be noted t h a t t h i s spectrum ranges from roughly 0.10 t o 0.30 eV with c e n t r a l v a l u e n e a r 0.20 eV. This i s i n good agreement with t h e p e a k - s h i f t r e s u l t s ; however, t h e range of a c t i v a t i o n e n e r g i e s i s g r e a t e r using the DSA method, probably because t h e p e a k - s h i f t method could n o t be used a c c u r a t e l y f o r the t a i l p o r t i o n s of t h e peaks.

The histogram approximation of the spectrum i n Fig. 3 i s very broad, covering n e a r l y seven o r d e r s of magnitude i n r e l a x a t i o n time. I n a d d i t i o n , t h e histogram appears t o be bell-shaped, s u g g e s t i n g a lognormal d i s t r i b u t i o n . A lognormal f i t t o t h e h i s t o - gram was made and r e s u l t e d i n the s o l i d curve i n Fig. 3. The width p2rameter f o r t h i s f i t is 8 ~ 4 . 8 3 , and the c e n t e r of the d i s t r i b u t i o n i s 'tm=4.05x10' s. Again, t h i s l a t t e r value i s i n good agreement w i t h the expectaEion v a l u e from experiments which f o r the temperature of the peak i s z=l/w=3.75~10- s.

I t should be pointed o u t t h a t the r e s u l t s shown i n Fig. 3 a r e one of t h e many d i f - f e r e n t DSA a n a l y s e s of the o r i g i n a l d a t a which were made i n o r d e r t o check on the r e p r o d u c i b i l i t y of t h e histogram approximations. I n a l l c a s e s the o t h e r a n a l y s e s gave r e s u l t s which agreed and showed c o n s i s t e n c y ~ i t h the r e s u l t s shown. Also, DSA was run on the d a t a shown i n Fig. 1 f o r ~ 4 7 7 5 s'

.

The histograms ca c u l a t e d show

₁

t h e same g e n e r a l shape, magnitude, and breadth a s those f o r -26640 s'

.

,,Thp lognormal f i t g i v e s $=5.02 and the d i s r i b u t i o n

_t

i s c e n t e r e d a t zm=2.1x10' s, which a g a i n a g r e e s w i t h z=l/w=2.09~10' s.

Since the r e l a x a t i o n - t i m e spectrum a s s o c i a t e d w i t h t h i s i n t e r n a l - f r i c t i o n peak can be approximated by a lognormal d i s t r i b u t i o n , i t i s p o s s i b l e t o use the published i n f o r m a t i o n about lognormal d i s t r i b u t i o n s to c a l c u l a t e the s p e c t r a l parameters d i r e c t l y from the i n t e r n a l - f r i c t i o n peak 141. These parameters can then be compared w i t h those obtained by t h e DSA method thus providing a f u r t h e r check on t h e analysis. The r e s u l t s of t h e s e c a l c u l a t i o n s a r e p r e s e n t e d i n Table 1 f o r both of t h e peaks i n Fig. 1. Comparison of the r e s u l t s f o r

p,

zm, and t h e r e l a x a t i o n s t r e n g t h o b t a i n e d by t h e s e two methods shows good agreement, t y p i c a l l y w i t h i n 5X, f o r each of t h e s e parameters.

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ACTIVATION ENERGY (eV)

0.05 0.10 0.15 0.20 0.25 0.30 0.35

/

R E L A ~ A T I O N - ~ I M E DIS;RIBUTION H I S T O ~ R A M

1

!

RELAXATION TIME, r ( s )

Fig. 3

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DSA r e l a x a t i o n time ( o r a c t i - v a t i o n energy) d i s t r i b u t i o n histogram from t h e d a t a i n Fig. 1 f o r ~ 2 6 6 4 0 s - l . Temperature of t h e d i s t r i b u t i o n

₁₉

130 K, and T O i s taken a s 5x10' s. The s p c t r a l l i m i t s f o r t h e calcu.lation a r e shown by the two v e r t i c a l d o t t e d l i n e s . The s o l i d curve shows a lognormal f i t t o t h e r e l a x a t i o n t i m spec-

trum w i t h 8-4.83 and h=4.05x10-5 s.

Fig. 4

-

DSA To d i s t r i b u t i o n histogram 1 from the d a t a i n Fig. 1 f o r -26640 s-

.

A c o n s t a n t a c t i v a t i o n energy of 0.205 eV was assumed. The s p e c t r a l l i m i t s a r e

shown by the two v e r t i c a l d o t t e d l i n e s . The s o l i d curve i s f o r a lognormal f i t t o t h e h i s to55am with $=4.81 and .cOm=4.43x10' s.

V

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DISCUSSION AND CONCLUSIONS

An i n t e r n a l f r i c t i o n peak due t o hydrogen i n NbV a t 8 a t . % H has been a n a l y z e d , c h i e f l y w i t h the DSA method. The r e s u l t s a r e c o n s i s t e n t w i t h an i n t e r p r e t a t i o n t h a t t h e f r i c t i o n i s due t o s t r e s s - i n d u c e d r e o r i e n t a t i o n , a Snoek-type mechanism. A l a r g e spread i n a c t i v a t i o n e n e r g i e s o b t a i n e d from 0.10 t o 0.30 eV i s r e f l e c t e d i n a peak width 3.3 times t h a t of a Debye peak ( s i n g l y a c t i v a t e d ) . This v a r i a t i o n i n ER i s i n t e r p r e t e d t o d e r i v e from a spread i n r e l a x a t i o n times f o r t h e r e o r i e n t i n g hydrogen owing t o a v a r i a t i o n i n the chemical s h o r t - r a n g e o r d e r p o s s i b l e i n t h i s a l l o y a t the i n t e r s t i t i a l s i t e s . The v a l u e of t h e DSA i s c l e a r l y demonstrated i n a system such a s t h i s where c l a s s i c a l a n a l y s e s based upon s i n g l y a c t i v a t e d p r o c e s s e s must break down.

Table 1: Parameters f o r D i s t r i b u t i o n of R e l a x a t i o n Times

*Assuming t h a t a lognormal d i s t r i b u t i o n $ and t h e r e l a x a t i o n s t r e n g t h can be o b t a i n e d from the peak width and h e i g h t , Ref. 4, p. 98.

Frequefcy

,

( s - 26640 4775

REFERENCES

/ I / Tanaka, S. and Koiwa, M., S c r i p t a Met. 15 (1981) 403.

/ 2 / Owen, C.V., Buck, 0. and S c o t t , T.E., s = i p t a Met.

15

(1981) 1097.

/3/ Weller, M., Zhang, J.X., L i , G.Y., Ke, T.S. and D i e h l , J., Acta Met.

29

(1981) 1055

Temperature (K) 130 119

141 Nowick, A.S. and Berry, B.S., A n e l a s t i c R e l a x a t i o n s i n C r y s t a l l i n e S o l i d s , Academic P r e s s . New York (1972).

/5/ Cost, J.R., N o n t r a d i t i o n a l Methods i n D i f f u s i o n , ed. by Murch, G., TMS-AIME, New York (1984).